A teacher’s role is to recommend or encourage the use of specific learning strategies that are the most beneficial for individual learners or the problem at hand. While no one learning strategy is perfect for all learners and all situations, PISA results indicate that students benefit throughout their schooling when they control their learning. Students who approach mathematics learning strategically are shown to have higher success rates on all types of mathematics problems, regardless of their difficulty.

WHAT ARE CONTROL STRATEGIES IN MATHEMATICS?

Control strategies are part of the METACOGNITION family of general approaches to learning. The two other strategy members of the metacognition family are memorization and elaboration. We talked about memorization strategies in Episode 12 and will talk about elaboration next episode.

Control strategies are learning strategies that allow students to set their own goals and track their own learning progress. In other words, control strategies are methods that help learners control their own learning.

This approach includes activities such as:

organizing material

creating a study plan and reflecting on the learning strategies used

activities related to concepts such as efficiency, strategic learning, self-regulation and metacognition.

PISA asked students questions that measured their use of control strategies in mathematics and found that students around the world tend to use control strategies to learn mathematics more than memorization or elaboration strategies (which is looked at in detail in Question 6).

The questions to measure a student’s tendency to use control strategies were:

When I study for a mathematics test, I try to work out what are the most important parts to learn.

When I study mathematics, I make myself check to see if I remember the work I have already done.

When I study mathematics, I try to figure out which concepts I still have not understood properly.

When I cannot understand something in mathematics, I always search for more information to clarify the problem.

When I study mathematics, I start by working out exactly what I need to learn.

Students in the United States reported using control strategies less than the OECD average…although it was just a little less than average. Countries at the top of the list (high use of control strategies) were China, Japan, Hong Kong…mathematical powerhouses. Countries at the bottom of the list were Jordan, Tunisia, Qatar. I’m not sure what to make of this because it is more complicated than just a matter of “good math teaching utilizes lots of control strategies”, because Korea, another math powerhouse, reported using control strategies far less than average.

WHAT IS THE BENEFIT OF STRATEGIC LEARNING IN MATHEMATICS?

Students who use control strategies more frequently score higher in mathematics than students who use other learning strategies such as memorization. What’s more, control strategies work equally well for nearly all mathematics problems, EXCEPT the most difficult ones.

I don’t understand this from the report:

Control strategies might not be as effective for solving the most complex mathematics problems because too much control and strategic learning might hinder students from tapping their creativity and engaging in the deep thinking needed to solve them.

I thought control strategies allow the student to be in control of his own learning and goals. So…I’m not too sure what this means.

What is taught in mathematics class and how learning is assessed might also limit the effectiveness of these strategies. Research suggests that the success of these strategies depends on what is being asked of students by their teachers, schools and education systems. For example, when students are only being assessed on surface-level knowledge of concepts, they won’t venture into deeper learning of mathematics on their own. Control strategies need to be practiced by the student on complex problems as well as easy ones.

IF CONTROL STRATEGIES ARE SO SUCCESSFUL, WHY SHOULDN’T I ENCOURAGE STUDENTS TO USE ONLY THESE LEARNING STRATEGIES AND NOTHING ELSE?

One size does not fit all!

Just as one teaching strategy doesn’t work for every student or every mathematical concept, control strategies aren’t appropriate for every student or every problem all the time.

Also, the use of control strategies is somewhat associated with great anxiety towards mathematics and less self-confidence.

Despite the negative characteristic associated with control strategies, students who report the highest use of control strategies score the highest on the PISA.

WHAT CAN TEACHERS DO?

Make sure that your own teaching doesn’t prevent students from adopting control strategies.

When teachers adopt certain teaching practices, they may be inadvertently reinforcing the use of certain learning strategies. For example, by giving homework that includes mathematics drilling exercises, you might be encouraging students to use memorization over control strategies.

Familiarise yourself with the specific activities in the category of “control strategies”.

Once you understand what constitutes a control strategy in mathematics, you can work to incorporate related activities into your teaching and encourage your students to use similar strategies themselves. For example, you might have your students work in groups to create a study plan for an upcoming exam and monitor their own progress.

Encourage students to reflect on how they learn.

Provide students with opportunities to discuss their problem-solving procedures with you and with their peers. Helping students develop a language with which to express their mathematical thinking can also help you better target any support you provide to your students.